It would depend on how acceptable his beliefs were to the missionaries and how diplomatic to the West. If he were more astute and diplomatic, he could have anticipated 1911 by guarranteeing the Western rights. Mid-19th century was generally an era of idealism, from the Abolitionists to the Geneva Conventions, and it's possible the prospect of a genuinely Christian China could have made the Western governments swallow the fear of the unknown and support the Taipings. As already been said, the degree of support would be proportional to how persuasive the assurances of status quo would be. In addition, it's important to note that the West was not yet a public issue beyond the small rarefied confines of the Confucian elite. Even in 1895, it was the elites more than the public who were incensed at Japan. If the Taipings were anti-Confucian, then their opinions wouldn't have mattered and as long as the land reforms were effected, peasants would have been satisfied. This would be doubly true at this time, because the West even then still did not penetrate China very much beyond a few Treaty ports. It was very much possible to let the foreigners alone and found a new, Christian dynasty.
Hong Xiuquan's beliefs will probably never be acceptable to the west. It's one thing for him to accept Christianity, it's another to completely warp it through his misunderstanding of it. To the West, the Taiping didn't represent Christian rebels against a repressive Chinese government. They were a radical sect aiming to overthrow the Qing, building upon anti-Qing sentiment that could be traced back to the 17th century. I don't think there's any way for Hong Xiuquan to water down his beliefs simply because it'd completely change the Taiping and who they were.
And I have little faith in one man precipitating the rise of a conservative concubine within the Qing Dynasty and pressing China down a road of further humiliation, not just by the West, but by Japan as well. After all, during the Taiping Rebellion, Japan was not too unlike China. American warships had forced her open and the Great Powers had forced unequal treaties upon them too. In fact, Japan was muddled while Prince Gong was beginning to organize the Self-Strengthening Movement. I don't think anyone in the west, let alone in China, had any idea what was about to happen down the next forty years, let along the rise of Republicanism and Warlordism and the ending of China's centuries old system by a rebellion by garrison troops (not unlike the similar revolts that had happened in the past decade: and
hell, in that same year, too).
Yeah, abolitionism and virulent racism and Imperialism, too. Geneva and two huge, destructive wars in the 20th century. I don't have much faith in the 19th centuries idealism. Because while ultimately the Western Powers probably don't care who is sitting on the throne in China, their capitalists, traders, and ect might react unfavorably if they end up getting shut out of their markets. Sure, they were confined to the Treaty Ports, but this period was also seeing an expansion of that. The Second Opium War saw the expansion of the five treaty ports to several others. The Foreign Legations were being opened in Beijing, and Britain especially had Consulates opened at Hankou, Takao, Tumsui, and of course Shanghai and Xiamen. The British would also begin operating the Chinese Imperial Maritime Customs Bureau, too. You're right that the Europeans are still mostly contained from the interior, but they were relatively free to do as they pleased, had extraterritoriality, opium was legalized, and missionaries were (typically) to do their work as they pleased.
I can see the public not having an issue with the west, after all, c. 1860, there really is no public opinion. China at that point has no middle class to speak of, unless you counted the Chinese Gentry and the Mandarins; illiteracy was widespread and China was a still very much an insular society. I would say despite Prince Gong's efforts, China remained an enclosed society until Emperor Guangxu. I would say it wasn't really until the abolition of the Imperial examinations and that Chinese students began to go abroad to study that public opinion began to be born and there was outrage against Japan or the West, with the overseas Chinese themselves playing a vital role. Before that, the average Chinese person was closed off in his own world and what the Imperial Court happened to do did not effect them in any way. Even the Opium War was not a huge psychological blow for the average Chinese person. The Imperial Government was humiliated as was it's class of mandarins and government bureaucrats, but I wouldn't think the average peasant in c. 1830 was heavily impacted by these events. I'd say the floods in the 1850s and other natural disasters were more important in causing the common people to become disillusioned with the Qing Dynasty.